Physics enhanced neural networks predict order and chaos

TL;DR

This paper introduces physics-enhanced neural networks that incorporate Hamiltonian structures to accurately predict phase space trajectories in nonlinear systems transitioning between order and chaos, demonstrating broad applicability.

Contribution

The paper presents a novel neural network architecture that embeds Hamiltonian dynamics, enabling accurate predictions in complex nonlinear systems exhibiting both order and chaos.

Findings

Successfully applied to Henon-Heiles system

Predicts phase space trajectories across order-chaos transition

Demonstrates potential for diverse scientific fields

Abstract

Conventional artificial neural networks are powerful tools in science and industry, but they can fail when applied to nonlinear systems where order and chaos coexist. We use neural networks that incorporate the structures and symmetries of Hamiltonian dynamics to predict phase space trajectories even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on the canonical Henon-Heiles system, which models diverse dynamics from astrophysics to chemistry. The power of the technique and the ubiquity of chaos suggest widespread utility.